st: xtnbreg meaning of r and s

[Owen Gallupe <ogallupe@gmail.com>]

Hello,

I am wondering how to interpret the "r", "s", "/ln_r", and "/ln_s"
rows when running a random effects negative binomial model. I see that
in the Stata documentation it states "In the random-effects model, the
dispersion varies randomly from group to group, such that the inverse
of one plus the dispersion follows a Beta(r; s) distribution." And
also "the /ln_r and /ln_s lines refer to ln(r) and ln(s), where the
inverse of one plus the dispersion is assumed to follow a Beta(r; s)
distribution."

Could anybody please interpret this in laymen terms? I would expect
that at least one of the rows relates to the between-cluster
differences in the dependent variable intercept, but the meaning of
these values are vague to me.

Please see example below (dependent variable is alcohol use, sample
clustered within schools):

xtnbreg alc age ses grades, i(school)

                 Coef.     Std. Err.         z      P>|z|      95%
Conf. Interval]

age       .1367576     .0262892     5.20    0.000     .0852318    .1882835
ses       .0725459     .0224051     3.24    0.001     .0286327    .1164591
grades   -.0265956   .0231602     -1.15   0.251     -.0719887    .0187975
_cons    .0270704    .0691694     0.39    0.696     -.108499      .1626398

/ln_r      4.084042    .3880532                             3.323472
  4.844613
/ln_s     3.923952    .4021785                             3.135697     4.712208

r           59.38505     23.04456                            27.75656
   127.0541
s          50.60003     20.35025                            23.00466
   111.2976


Thank you.

Owen Gallupe

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